Weather-Resilient Countermeasures for Line-of-Sight Multiple-Input Multiple-Output Feeder Links in Multibeam Satellite Systems

ABSTRACT

A system and method for providing multi-input multi-output (MIMO) feeder links for a multibeam satellite system. The method includes configuring a X×Y MIMO antenna system using X-antennae having dominant line-of-sight (LoS) of Y-antennae; transmitting, simultaneously, a Tx signal as X Tx signals on a MIMO channel with the X-antennae; receiving the X Tx signals on the MIMO channel with the Y-antennae as Y Rx signals, wherein each of the Y-antennae generate one of the Y Rx signals; and ground-interference processing the X Tx signals or the Y Rx signals to recover the Tx signal; satellite-interference processing the X Tx signals or the Y Rx signals to recover the Tx signal. In the method, the ground interference processing includes countermeasures as either pre-interference processing when the X-antennae are disposed on a ground or post-interference processing when the X-antennae are disposed in a Geosynchronous orbit satellite. Gateway diversity for multiple MIMO feeder links utilizing these countermeasures improves weather-resiliency and significantly enhances overall satellite network availability.

CROSS-REFERENCE TO RELATED APPLICATIONS AND INCORPORATION BY REFERENCE

The present application is a continuation of U.S. patent applicationSer. No. 17/452,547, filed Oct. 27, 2021 and claims the benefit under 35U.S.C. 119(e) of U.S. Provisional Application Ser. No. 63/169,773, filedApr. 1, 2021, which are incorporated herein by reference in theirentireties.

FIELD

A method and multibeam satellite system achieving substantialorthogonality between spatially multiplexed signals with multiplemulti-input multi-output (MIMO) feeder links operating in line-of-sight(LoS) channels using essentially a common spot beam per link isdisclosed. Countermeasures against inter-antenna interference based onlinear pre-interference and post-interference signal processing providegains in signal-to-noise ratio, spatial multiplexing, and spatialdiversity. Comparisons of linear versus circular pattern spacing for agateway cluster, including variations in gateway array orientations,provide flexibility in locating gateway installation sites. Gatewaydiversity for multiple MIMO feeder links utilizing these countermeasuresimproves weather-resiliency and significantly enhances overall satellitenetwork availability.

BACKGROUND

The prior art multibeam satellite systems using MIMO requirescatter-rich channels, such as typically found in terrestrial wirelessnetworks. Moreover, low-Earth orbit (LEO) applications operate in ascatter-rich environment, resulting from Ricean fading with a low Ricefactor. However, LoS conditions, rather than scatter-rich, areencountered in geostationary satellite systems, traditionally limitingthe usefulness of MIMO for geostationary Earth orbit (GEO) applications.

Some prior art satellites systems use multiple satellites with one MIMOantenna each, a very costly alternative. Other prior art systems employsmart gateway diversity but only using Single In Single Out (SISO)feeder links, not taking advantage of cooperation among the multipletransmit and receive antennas.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that is further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter.

The present teachings achieve substantial spatial orthogonality ofindependent signals transmitted in MIMO-enabled satellite systems withLoS channels, when these signals use the same time, frequency, andpolarization resources. A single satellite with multiple reflectors isneeded. For a given geographic area, the teachings allow more gatewaysto be placed with acceptable interference levels among them. For a givenavailability requirement, significantly enhanced overall satellitenetwork availability against severe weather impairments relative tostate-of-the-art SISO feeder links can be achieved.

A system of one or more computers can be configured to performparticular operations or actions by virtue of having software, firmware,hardware, or a combination of them installed on the system that inoperation causes or cause the system to perform the actions. One or morecomputer programs can be configured to perform particular operations oractions by virtue of including instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the actions. Onegeneral aspect includes a method for providing multi-input multi-output(MIMO) feeder links for a multibeam satellite system. The methodincludes configuring a X×Y MIMO antenna system using X-antennae havingdominant line-of-sight (LoS) of Y-antennae; transmitting,simultaneously, a Tx signal as X Tx signals on a MIMO channel with theX-antennae; receiving the X Tx signals on the MIMO channel with theY-antennae as Y Rx signals, wherein each of the Y-antennae generate oneof the Y Rx signals; and ground-interference processing the X Tx signalsor the Y Rx signals to recover the Tx signal; satellite-interferenceprocessing the X Tx signals or the Y Rx signals to recover the Txsignal. In the method the ground interference processing includescountermeasures as either pre-interference processing when theX-antennae are disposed on a ground or post-interference processing whenthe X-antennae are disposed in a Geosynchronous orbit satellite, thesatellite interference processing includes a passthrough when arespective Signal-to-Interference-and-Noise Ratio (SINR) of each of theY Rx signals is greater than a threshold, and a channel capacity of theMIMO channel is greater than a channel capacity of a Single-InputSingle-Output (SISO) channel having resources identical to the MIMOchannel. Implementations may include one or more of the followingfeatures.

The method where X and Y are equal.

The method where the satellite interference processing includescountermeasures when the respective SINR of each of the Y Rx signals isless than or equal to the threshold.

The method where the countermeasures are based on one or more of, aweighted or non-weighted version of, a Zero-Forcing (ZF) criteria, aMinimum Mean-Square Error (MMSE) criteria, or a regularized ZF (RZF)criteria.

The method where the countermeasures are based on high-quality channelstate information (CSI) about signal propagation on the MIMO channel.

The method where the Y-antennae are disposed in the Geosynchronous orbitsatellite, the respective SINR of each of the Y Rx signals less than orequal to the threshold, the satellite interference processing includescountermeasures, the ground interference processing uses an identitymatrix, and weather between one of the X-antennae and the Y-antennaeexceeds a precipitation-induced outage limit.

The method where the Y-antennae are disposed on the ground, therespective SINR of each of the Y Rx signals less than or equal to thethreshold, the satellite interference processing includes a passthrough,the ground interference processing uses a non-identity matrix, andweather between one of the X-antennae and the Y-antennae exceeds aprecipitation-induced outage limit.

The method where when weather, between Z of the X-antennae and theY-antennae, exceeds a precipitation-induced outage limit, Z diversityantennae are substituted for the one of the X-antennae or the Y-antennaeon the ground, the X×Y MIMO antenna system operates as a (X−Z)×Y orX×(Y−Z) MIMO antenna system, and Z is greater than or equal to 1.

The method where the X-antennae form a cluster, the multibeam satellitesystem includes M clusters, associating each of the M clusters with arespective Tx signal, each of the clusters transmitting over the MIMOchannel simultaneously, M times the channel capacity of the MIMO channelis greater than M times the channel capacity of the SISO channel, and Mis greater than 1.

The method where the clusters are separated from each other by adistance greater than 100 kilometers.

The method where either the Y-antennae or the X-antennae are spaced in asubstantially linear formation on the ground and spaced from one anotherby a distance of less than 50 kilometers.

The method where either the Y-antennae or the X-antennae are spaced in asubstantially circular formation on the ground and spaced from oneanother by a distance of less than 50 kilometers.

The method where either the Y-antennae or the X-antennae are spaced in asubstantially linear formation on the Geosynchronous orbit satellite.

The method where either the Y-antennae or the X-antennae are spaced in asubstantially circular formation on the Geosynchronous orbit satellite.

The method where the X-antennae are interconnected via a fiber ormicrowave link, and spaced on the ground within an acceptable range ofan optimal position.

The method where the Y-antennae are interconnected via a fiber ormicrowave link, and spaced on the ground within an acceptable range ofan optimal position.

The method where the X Tx signals are substantially orthogonal at theY-antennae.

The method where implementations of the described techniques may includehardware, a method or process, or computer software on acomputer-accessible medium.

Additional features will be set forth in the description that follows,and in part will be apparent from the description, or may be learned bypractice of what is described.

DRAWINGS

In order to describe the manner in which the above-recited and otheradvantages and features may be obtained, a more particular descriptionis provided below and will be rendered by reference to specificembodiments thereof which are illustrated in the appended drawings.Understanding that these drawings depict only typical embodiments andare not, therefore, to be limiting of its scope, implementations will bedescribed and explained with additional specificity and detail with theaccompanying drawings.

FIG. 1A illustrates a MIMO-enabled feeder link for a multibeam satellitesystem including a cluster using a linear formation according to variousembodiments.

FIG. 1B illustrates a MIMO-enabled feeder link for a multibeam satellitesystem including a cluster using a circular formation according tovarious embodiments.

FIG. 1C illustrates a multibeam satellite system including multipleclusters according to various embodiments.

FIG. 2A illustrates a 3D capacity of 3×3 MIMO uplink and downlink feederlinks in the E-band against a gateway separation when using a lineargateway formation according to various embodiments.

FIG. 2B illustrates a 3D capacity of 3×3 MIMO uplink and downlink feederlinks in the E-band against a gateway separation when using a circulargateway formation according to various embodiments.

FIG. 3 illustrates countermeasures for MIMO feeder uplinks according tovarious embodiments.

FIG. 4 illustrates countermeasures for MIMO feeder downlinks accordingto various embodiments.

FIG. 5A, FIG. 5B and FIG. 5C illustrate Uplink SINR performance of a 3×3MIMO feeder link with a linear gateway formation when usingpre-interference processing, post-interference processing, and pre- andpost-interference processing, respectively, according to someembodiments.

FIG. 6A, FIG. 6B and FIG. 6C illustrate Uplink SINR performance of a 3×3MIMO feeder link with a circular gateway formation when usingpre-interference processing, post-interference processing, and pre- andpost-interference processing, respectively, according to someembodiments.

FIG. 7A, FIG. 7B and FIG. 7C illustrate Uplink SINR performance of a 3×3MIMO feeder link with a linear gateway formation when the third gatewayexperiences a 10-dB rain attenuation and using pre-interferenceprocessing, post-interference processing, and pre- and post-interferenceprocessing, respectively, according to some embodiments.

FIG. 8A, FIG. 8B and FIG. 8C illustrate Uplink SINR performance of a 3×3MIMO feeder link with a circular gateway formation when the thirdgateway experiences a 10-dB rain attenuation and using pre-interferenceprocessing, post-interference processing, and pre- and post-interferenceprocessing, respectively, according to some embodiments.

FIG. 9A and FIG. 9B illustrate Uplink sum-rate performance of 3×3 MIMOfeeder link in clear sky when using a linear and circular gatewayformation, respectively, according to some embodiments.

FIG. 10A and FIG. 10B illustrate Uplink sum-rate performance of 3×3 MIMOfeeder link when the third gateway experiences a 10-dB rain attenuationand using a linear and circular gateway formation, respectively,according to some embodiments.

FIG. 11A and FIG. 11B illustrate capacity of 3×3 MIMO feeder link as itvaries against inter-gateway separation and orientation when using alinear and circular gateway formation, respectively, according to someembodiments.

FIG. 12 illustrates outage probability comparison of 3×3 MIMO with SISOfeeder links, according to some embodiments.

FIG. 13 illustrates overall network outage probability comparison ofmultiple 3×3 MIMO with SISO feeder links, according to some embodiments.

Throughout the drawings and the detailed description, unless otherwisedescribed, the same drawing reference numerals will be understood torefer to the same elements, features, and structures. The relative sizeand depiction of these elements may be exaggerated for clarity,illustration, and convenience.

DETAILED DESCRIPTION

The present teachings may be a system, a method, and/or a computerprogram product at any possible technical detail level of integration.The computer program product may include a computer readable storagemedium (or media) having computer readable program instructions thereonfor causing a processor to carry out aspects of the present invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as SMALLTALK, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

Reference in the specification to “one embodiment” or “an embodiment” ofthe present invention, as well as other variations thereof, means that afeature, structure, characteristic, and so forth described in connectionwith the embodiment is included in at least one embodiment of thepresent invention. Thus, the appearances of the phrase “in oneembodiment” or “in an embodiment”, as well any other variations,appearing in various places throughout the specification are notnecessarily all referring to the same embodiment.

Introduction

The present teachings achieve substantial spatial orthogonality ofindependent signals transmitted in MIMO-enabled satellite systems withLoS channels, when these signals use the same time, frequency, andpolarization resources. A single satellite with multiple reflectors isneeded. For a given geographic area, the teachings allow more gatewaysto be placed with acceptable interference levels among them. For a givenavailability requirement, significantly enhanced overall satellitenetwork availability against severe weather impairments relative tostate-of-the-art SISO feeder links can be achieved.

Herein, a gateway refers to an antenna and a Radio Frequency Transceiver(RFT). The RFT may be connected to a data processor, via microwaves,fiber, or the like. The gateway may be remote from the data processor.For MIMO implementations, a group of gateways form a cluster. Eachgateway of a cluster connects to the same data processor. Each gatewayof a cluster is disposed on the ground in the same general vicinity, forexample, Nevada, Montana. Optimal distances between adjacent gateways ofa cluster may range from 10 to hundred kilometers. Distances betweenclusters may range in 100 s of kilometers. The gateways of a cluster maybe disposed in a linear, circular, or other polygon shapedconfiguration.

Due to the susceptibility of extremely high frequency (EHF) band toweather impairments, a multiple gateway configuration provides gatewaydiversity. P diversity MIMO feeder links maybe added per N primaryfeeder links to achieve redundancy. Data rerouting from one gateway toanother may be implemented when experiencing deep rainfall events tomeet overall network availability targets. The MIMO-enabled feeder linksoffer large margin of protection against rain attenuation, resulting ingreatly enhanced overall satellite network availability, when comparedwith the prior art single-input single-output (SISO) feeder links.

FIG. 1A illustrates a MIMO-enabled feeder link for a multibeam satellitesystem including a cluster using a linear formation according to variousembodiments.

FIG. 1A illustrates an exemplary satellite network 100 that implementsfeeder links using a M_(g)×M_(s) MIMO including a cluster 114. Satellitenetwork 100 includes M_(s) satellite antennae 104 ₀ to 104 _(s) at asatellite (not shown) separated by a distance d_(s) that are radiatingM_(s) highly overlapping beams 112. The M_(s) satellite antennae 104 ₀to 104 _(s) are connected to a satellite interference processor 103. Aground portion of the satellite network 100 includes the cluster 114including M_(g) gateways 102 ₀ to 102 _(g) separated by a distance d_(g)and disposed in a linear formation. Although, the satellite antennae 104₀ to 104 _(s) are illustrated in a linear formation, circular or otherformations may be used. The M_(g) gateways 102 ₀ to 102 _(g) areinter-connected to a ground interference processor 110. The groundinterference processor 110 may be disposed at a data processing center.Each of the M_(g) gateways 102 ₀ to 102 _(g) serves the M_(s) satelliteantennae 104 ₀ to 104 _(s) simultaneously, and vice-versa. Both uplinks106 and downlinks 108 on the feeder side are provided by the beams 112.For uplinks 106, the gateways 102 ₀ to 102 _(g) may radiate multiple LoSand highly overlapping beams (not shown, for example, 3 beams in the 3×3MIMO formation) towards the satellite antennae 104 ₀ to 104 _(s). Fordownlinks 108, the satellite antennae 104 ₀ to 104 _(s) may radiatemultiple LoS and highly overlapping beams 112 towards the gateways 102 ₀to 102 _(g). In some embodiments, the gateways 102 ₀ to 102 _(g) includemulti-feed antennae. In some embodiments, the satellite antennae 104 ₀to 104 _(s) include multi-feed antennae.

FIG. 1B illustrates a MIMO-enabled feeder link for a multibeam satellitesystem including a cluster using a circular formation according tovarious embodiments.

FIG. 1B illustrates an exemplary satellite network 100 that implementsfeeder links using a M_(g)×M_(s) MIMO including a cluster 114. Satellitenetwork 100 includes M_(s) satellite antennae 104 ₀ to 104 _(s) at asatellite (not shown) separated by a distance d_(s) that are radiatingM_(s) highly overlapping beams 112. The M_(s) satellite antennae 104 ₀to 104 _(s) are connected to a satellite interference processor 103. Aground portion of the satellite network 100 includes the cluster 114including M_(g) gateways 102 ₀ to 102 _(g) separated by a distance d_(g)and disposed in a circular formation. The M_(g) gateways 102 ₀ to 102_(g) are arranged to form a triangle on the ground for illustrationonly. The M_(g) gateways 102 ₀ to 102 _(g) are inter-connected to aground interference processor 110. The ground interference processor 110may be disposed at a data processing center. Each of the M_(g) gateways102 ₀ to 102 _(g) serves the M_(s) satellite antennae 104 ₀ to 104 _(s)simultaneously, and vice-versa. Both uplinks 106 and downlinks 108 onthe feeder side are provided by the beams 112.

FIG. 1C illustrates a multibeam satellite system including multipleclusters according to various embodiments.

A multibeam satellite system 130 may include a satellite 132 andclusters 136 disposed around a coverage area 134. The satellite 132 mayinclude M_(s) antennae (not shown). Each cluster 136 may include M_(g)gateways (not shown). Gateways of each cluster 136 may be disposed in aformation dictated by the local geography. Gateways of each cluster 136may be disposed in a formation different than formations used by otherclusters. Gateways of more than one of the clusters 136 may use the sameresources, for example, satellite, frequency, time, polarization, tocommunicate with the M_(s) satellite antennae using beams 138. Each ofthe beams 138 may have been subjected to countermeasures describedherein.

Exemplary cluster placements in the coverage area 134 are used below forease of description and are not limiting. Assuming that cluster 136 a ofMontana, US and cluster 136 b of Nevada, US use the same resources.Beams 138 a communicate with each gateway of cluster 136 a. Beams 138 aare based on a first source signal (not shown), either received ortransmitted simultaneously by the gateways of the cluster 136 a, beingprocessed by a first data processor (not shown) provided for the cluster136 a. Similarly beams 138 b are based on a second source signalprocessed by a second data processor that is different than the firstdata processor. The first source signal is different than the secondsource signal. Although, the beams 138 a of each gateway of the cluster136 a are based on the first source signal, each of the beams 138 aconveyed by the multibeam satellite system 130 may be distinct as eachmay have been subjected to different countermeasures described herein.Other beams 138 are formed in the manner beam 138 a are formed.

System Model

A geostationary Earth-orbiting (GEO) satellite system on a feeder-linkside, in both the uplink and downlink directions, may benefit from a LoSMIMO capability. The satellite may be equipped with M_(s) multi-feedreflector antennas with high directivity. A ground network may include agroup of M_(g) gateways cooperating via terrestrial inter-connections todata processors. The gateways may share the same time, frequency, andpolarization resources. A total of N such MIMO-enabled feeder links maybe used throughout the coverage area to provide a massive overallsatellite network throughput. The separation of the feeder links may bein tens of kilometers per FIG. 2A and FIG. 2B. Embodiments where theseparation of the feeder links may be the order of hundreds ofkilometers to reduce spatial interference among them may also be used.In some embodiments, the EHF range of the electromagnetic spectrum isutilized, including 81-86 GHz for the feeder uplink and 71-76 GHz on thefeeder downlink.

FIG. 1A and FIG. 1B illustrate an individual MIMO-enabled feeder link ina multi-beam satellite system. A feed in each reflector antenna is usedto point highly overlapping beams over a multiplicity of gateways,configured in either linear or circular formations. Assuming the orbitallocation of the satellite on the equator with a longitudinal slot ofθ_(s) and a linear formation for the satellite antennae with uniformspacing of d_(s,m) then the position vector, α_(s,m) of the mth antennain a 3D Cartesian coordinate system is

$\begin{matrix}{{{\underline{a}}_{s,m} = \begin{bmatrix}{{R_{s} \cdot {\cos( \theta_{s} )}} - {d_{s,m} \cdot {\sin( \theta_{s} )}}} \\{{R_{s} \cdot {\sin( \theta_{s} )}} + {d_{s,m} \cdot {\cos( \theta_{s} )}}} \\0\end{bmatrix}},} & (1)\end{matrix}$

where R_(s) is the GEO radius, and d_(s,m) is the spacing between thecenter of the antenna array onboard the satellite and its mth antennam=1, 2, . . . , M_(s) where

$\begin{matrix}{d_{s,m} = {d_{s} \cdot {( {m - \frac{1}{2} - \frac{M_{s}}{2}} ).}}} & (2)\end{matrix}$

On the ground, the cluster of gateways can be configured in twodifferent formations: linear versus circular. For the linear spacingpattern illustrated in FIG. 1A, the uniform spacing for the nth feederlink is d_(g) ^((n)). The center of the gateway cluster has latitude andlongitude coordinates of Φ_(g) ^((n)) and θ_(g) ^((n)), respectively,whereas the orientation δ_(g) ^((n)) is the angle between the east-westdirection and the gateway cluster. Then, the position vector, α _(g,m)^((n)), of the mth gateway belonging to the _(n)th feeder link in a 3DCartesian coordinate system is

${\underline{a}}_{s,m}^{(n)} = {{\begin{bmatrix}{R_{g}{\cos( {{\phi_{g}^{(n)}{\cos( \theta_{g}^{(n)} )}} - {d_{g,m}^{(n)}( {{{\sin( \theta_{g}^{(n)} )}{\cos( \delta_{g}^{(n)} )}} + {{\sin( \phi_{g}^{(n)} )}{\cos( \theta_{g}^{(n)} )}{\sin( \delta_{g}^{(n)} )}}} )}} }} \\{R_{g}\cos( {{\phi_{g}^{(n)}{\sin( \theta_{g}^{(n)} )}} + {d_{g,m}^{(n)}( {{{\cos( \theta_{g}^{(n)} )}{\cos( \delta_{g}^{(n)} )}} - {{\sin( \phi_{g}^{(n)} )}{\sin( \theta_{g}^{(n)} )}{\sin( \delta_{g}^{(n)} )}}} )}} } \\{{R_{g}{\sin( \phi_{g}^{(n)} )}} + {d_{g,m}^{(n)}{\cos( \phi_{g}^{(n)} )}{\sin( \delta_{g}^{(n)} )}}}\end{bmatrix},}}$

where R_(g) is the Earth radius and d_(g,m) ^((n)) is the spacingbetween the center of the gateway cluster and the mth gateway m=1, 2, .. . , M_(s) where

$\begin{matrix}{d_{g,m}^{(n)} = {g_{g}^{(n)} \cdot {( {m - \frac{1}{2} - \frac{M_{g}}{2}} ).}}} & (4)\end{matrix}$

For the circular spacing pattern illustrated in FIG. 1(b), the gatewaysmay be spaced with a separation of d_(g) ^((n)) for the nth feeder link.Let Φ_(g) ^((n)) and θ_(g) ^((n)) be the latitude and longitude of thecenter of the gateway formation on the ground, respectively, whereasδ_(g) ^((n)) be the orientation associated with the first gatewayrelative to the East-West direction. Then, the position vector α _(g,m)^((n)), of the mth gateway belonging to the nth feeder link in a 3DCartesian coordinate system and the orientation of the mth gateway are

$\begin{matrix}{{\underline{a}}_{s,m}^{(n)} = {{\begin{bmatrix}{{R_{g}{\cos( \phi_{g}^{(n)} )}{\cos( \theta_{g}^{(n)} )}} - {\frac{d_{g}^{(n)}}{2{\sin( {\pi/M_{g}} )}}( {{{\sin( \theta_{g}^{(n)} )}{\cos( \delta_{g,m}^{(n)} )}} + {{\sin( \phi_{g}^{(n)} )}{\cos( \theta_{g}^{(n)} )}{\sin( \delta_{g,m}^{(n)} )}}} )}} \\{{R_{g}\cos( \phi_{g}^{(n)} ){\sin( \theta_{g}^{(n)} )}} + {\frac{d_{g}^{(n)}}{2{\sin( {\pi/M_{g}} )}}( {{{\cos( \theta_{g}^{(n)} )}{\cos( \delta_{g,m}^{(n)} )}} - {{\sin( \phi_{g}^{(n)} )}{\sin( \theta_{g}^{(n)} )}{\sin( \delta_{g,m}^{(n)} )}}} )}} \\{{R_{g}{\sin( \phi_{g}^{(n)} )}} + {\frac{d_{g}^{(n)}}{2{\sin( {\pi/M_{g}} )}}{\cos( \phi_{g}^{(n)} )}{\sin( \delta_{g,m}^{(n)} )}}}\end{bmatrix}{and}}}} & (5)\end{matrix}$ $\begin{matrix}{\delta_{g,m}^{(n)} = {\delta_{g}^{(n)} + {\frac{2\pi}{M_{g}} \cdot {( {m - 1} ).}}}} & (6)\end{matrix}$

In a linear formation, the gateways have the same orientation butlinearly increasing separation relative to the first gateway. Incontrast, a circular formation provides equal separation among thegateways but linearly increasing orientation relative to the firstgateway.

Countermeasures Against Mimo Inter-Antenna Interference Mimo ChannelModel and Capacity

In free-space, the complex-valued baseband response between the mthtransmit gateway and the nth satellite antenna is

$\begin{matrix}{{h_{m,n} = {\frac{\lambda_{n}}{4{\pi \cdot r_{m,n}}} \cdot {\exp( {{- j}{\frac{2\pi}{\lambda_{n}} \cdot r_{m,n}}} )}}},} & (7)\end{matrix}$

where λ_(u) is the wavelength associated with the uplink carrierfrequency and r_(m,n) is the distance between the two elements. Assumingthat the relative differences in path-loss are negligible, thenormalized free-space channel response matrix for an M_(s)×M_(g)MIMO-enabled feeder link is

$\begin{matrix}{H_{u,{LoS}}^{(n)} = \text{?}} & (8)\end{matrix}$ ?indicates text missing or illegible when filed

In clear-sky conditions, the feeder uplink channel model may be mademore complete to account for the radiation patterns of the satelliteantennas, providing as {tilde over (H)}_(u) ^((n)) as

{tilde over (H)} _(u) ^((n)) =J _(u) ⊙H _(u,Los) ^((n)),  (9)

where J_(u) has entries computed based on

$\begin{matrix}{{g_{u}( \theta_{o} )} = {{\frac{1}{2} \cdot \frac{\lambda_{n}}{\pi{D \cdot {\sin( \theta_{o} )}}} \cdot {J_{1}( {\pi{\frac{D}{\lambda_{u}} \cdot {\sin( \theta_{o} )}}} )}} + {36 \cdot ( {\frac{\lambda_{u}}{\pi{D \cdot {\sin( \theta_{o} )}}}{\text{?} \cdot {{J_{3}( {\pi{\frac{D}{\lambda_{n}} \cdot {\sin( \theta_{o} )}}} )}.}}} }}} & (10)\end{matrix}$ ?indicates text missing or illegible when filed

In (10), J₁(x) and J₃(x) are the Bessel functions of the first and thirdorder, respectively, θ₀ represents the off-axis angle relative toboresight, and D is the diameter of the satellite antennas. The uplinksignal vector as received by the satellite antennas, y _(s) ^((n)), isthen

y _(s) ^((n)) ={tilde over (H)} _(u) ^((n))Λ_(u) ^((n)) ·x _(g) ^((n)) w_(u) ^((n)),  (11)

where x_(g) ^((n)) is the vector of symbols transmitted by the gateways,w _(u) ^((n)) is the additive white Gaussian noise (AWGN) uplink noisewith variance σ_(u) ², and ∧_(u) ^((n)) is a diagonal matrix composed ofthe weather-induced attenuations, ξ_(m) _(g) ^((n)), affecting thegateways, or

Λ_(u) ^((n))=diag{ξ₁ ^((n))ξ₂ ^((n)), . . . ,ξ_(M) _(g) ^((n))},  (12)

derived from the attenuations A_(m) _(g) ^((n)) in decibel (dB) as A_(m)_(g) ^((n))=−20·log₁₀(|ξ_(m) _(g) ^((n))|).

Based on the received uplink signal in (11), the time-invariant MIMOchannel capacity is

C _(u) ^((n))=log₂(det(I _(M) _(g) +ρ_(u) ^((n)) ·{tilde over (H)} _(u)^((n))Λ_(u) ^((n))({tilde over (H)} _(u) ^((n))Λ_(u)^((n)))^(H))),  (13)

where ρ_(u) ^((n)) is the Carrier-to-Noise Ratio (CNR) on the uplinkthat includes the transmit power per gateway antenna.

Similar to (9), an M_(s)×M_(g) feeder downlink channel matrix, {tildeover (H)}_(d) ^((n)) can be defined based on the downlink wavelengthλ_(d) and the radiation patterns of the downlink beams J_(d) as

{tilde over (H)} _(d) ^((n)) =H _(d,Los) ^((n)) ⊙J _(d)  (14)

The corresponding downlink signal vector is

y _(s) ^((n))=Λ_(d) ^((n)) {tilde over (H)} _(d) ^((n)) ·x _(s) ^((n))+w _(d) ^((n)),  (15)

where x _(s) ^((n)) is the vector of symbols transmitted by thesatellite antennas and w _(d) ^((n)) is the AWGN downlink noise withvariance σ_(d) ². Its associated MIMO channel capacity is given by

C _(d) ^((n))=log₂(det(I _(M) _(g) +ρ_(d) ^((n))·(Λ_(d) ^((n)) {tildeover (H)} _(d) ^((n)))^(H)Λ_(d) ^((n)) {tilde over (H)} _(d)^((n)))),  (16)

where ρ_(d) ^((n)) is the downlink CNR. In (16), a property is appliedthat det(I+AB)=det(I+BA) if AB is complex conjugate symmetric.

A MIMO satellite channel can be improved by changing a gateway clustergeometry relative to the satellite antennas. In pure LoS MIMOconditions, explicit criteria in terms of the inter-antenna spacing arederived to ensure full spatial multiplexing gain.

FIG. 2A illustrates a 3D capacity of 3×3 MIMO uplink and downlink feederlinks in the E-band against a gateway separation when using a lineargateway formation according to various embodiments.

FIG. 2B illustrates a 3D capacity of 3×3 MIMO uplink and downlink feederlinks in the E-band against a gateway separation when using a circulargateway formation according to various embodiments.

FIG. 2A and FIG. 2B illustrate exemplary 3D capacity plots of a 3×3MIMO-enabled feeder link as it varies over the gateway separation whenthe carrier frequency ranges in 81-86 GHz for the uplink and 71-76 GHzfor the downlink at a CNR of 24 dB. Selected geometric gateway positionscan maximize the multiplexing gain in LoS conditions, resulting inachieving full-rank MIMO channel. For an inter-antenna spacing onboardthe satellite of 6 m, greater channel capacity is achieved when theinter-gateway distance is about 17 km and 43 km for the linear andcircular formations, respectively. Larger optimal gateway separation ismore advantageous in terms of decorrelating the rainfall events as it isless likely that more than two gateways separated by large distanceswill experience deep rain attenuations simultaneously.

Pre-Interference and Post-Interference Processing

FIG. 3 illustrates countermeasures for MIMO feeder uplinks according tovarious embodiments.

Countermeasures 300 against inter-antenna interference for MIMO-enabledfeeder links in the uplink direction may take the form ofpre-interference signal processing 302 (G_(pre) ^((n))) andpost-interference processing 314 (S_(post) ^((n))). Pre-interferencesignal processing 302 may be implemented on the ground 322 and maymaximize spatial multiplexing afforded by MIMO 324 for a normal weather,for example, a clear sky. This is done by performing a linearcombination of the gateway transmissions 308 (x _(g) ^((n))), at a dataprocessor through multiplication by pre-interference signal processing302 (G_(pre) ^((n))) to provide a modified transmitted vector 306({tilde over (x)} _(g) ^((n))), as

( {tilde over (x)} _(g) ^((n)))=(G _(pre) ^((n)))·( {tilde over (x)}_(g) ^((n))).  (17)

A normalization of pre-interference signal processing 302 (G_(pre)^((n))) may be used to ensure that the maximum power P_(u) ^((n))) ateach gateway is not exceeded. A post-interference processing 314 mayremove the spatial interaction 304 among the satellite receive antennas326 induced as a received signal 312 (y _(s) ^((n))) experiencesdifferent weather conditions 310 (w _(u) ^((n))). In some embodiments, alinear combination of the received signals onboard the satellite throughmultiplication by the post-interference processing 314 (S_(post) ^((n)))is performed to provide a modified received vector 316 ({tilde over (y)}_(s) ^((n)))

{tilde over (y)} _(s) ^((n)) =S _(post) ^((n)) ·y _(s) ^((n)).  (18)

In some embodiments, the pre-interference signal processing 302 (G_(pre)^((n))) based on a peak-power constraint is

G _(pre) ^((n))=√{square root over (P _(u) ^((n)))}·V _(u) ^((n))Q,  (19)

where V_(u) ^((n)) is the matrix containing as columns the eigenvectorsassociated with ({tilde over (H)}_(u) ^((n)))^(H)({tilde over (H)}_(u)^((n))) and Q is the unitary discrete Fourier transform (DFT) matrix.The post-interference matrix may be derived under the zero-forcing (ZF)condition as the left-inverse of a cascade of matrices, or

$\begin{matrix}{\text{?}} & (20)\end{matrix}$ ?indicates text missing or illegible when filed

The associated uplink signal-to-interference-and-noise ratio (SINR) isthe same across m_(g) and is computed as

$\begin{matrix}{{SINR}_{u,m_{g}}^{(n)} = {{SINR}_{u,{clear}}^{(n)} \cdot ( {\frac{1}{M_{g}}{\sum\limits_{i = 1}^{M_{g}}10^{({A_{i}^{(n)}/10}}}} )^{- 1}}} & (21)\end{matrix}$

where SINR_(u,clear) ^((n)) is the uplink SINR obtained under clear sky.

In some embodiments, useful in heavy precipitation, onlypost-interference processing is used which offers different SINRperformance depending on rain attenuation A_(m) _(g) ^((n)) that isaffecting any individual gateway. A scaled identity matrix may beselected for pre-interference processing, G_(pre) ^((n))=√{square rootover (P _(u) ^((n)))}·I_(m) _(g) in (17) and (20). The associated SINRperformance for implementing post-interference processing alone is

$\begin{matrix}{{{SINR}_{u,m_{g}}^{(n)} = {{SINR}_{u,{clear},m_{g}}^{(n)} \cdot 10^{({- A_{m_{g}}^{(n)}/10})}}},} & (22)\end{matrix}$

where SINR_(u,clear,m) _(g) ^((n)) the uplink SINR in clear skyassociated with the m_(g)th gateway, possibly different under thepost-processing solution, for m_(g)=1, 2, . . . , M_(g).

The achievable sum-rate for a given MIMO feeder link can then bedetermined for Gaussian symbols as

$\begin{matrix}{\mathcal{R}^{(n)} = {\sum\limits_{m_{g} = 1}^{M_{g}}{\log_{2}( {1 + {SINR}_{u,m_{g}}^{(n)}} )}}} & (23)\end{matrix}$

Countermeasures 300 based on ZF criterion are expected to achievenear-capacity performance as the noise levels are low on the feeder-linkside. In some embodiments, countermeasures 300 may be based on, forexample, minimum mean-square error (MMSE) or regularized ZF (RZF) toreduce amplification of noise components.

FIG. 4 illustrates countermeasures for MIMO feeder downlinks accordingto various embodiments.

Similarly on the downlink, countermeasures 400 against inter-antennainterference for MIMO-enabled feeder links includes pre-interferenceprocessing 402 (S_(pre) ^((n))) and post-interference signal processing414 (G_(post) ^((n))). Pre-interference processing 402 is implemented tomaximize spatial multiplexing afforded by MIMO in clear sky. A linearcombination of the satellite transmissions through multiplication bypre-interference processing 402 (S_(pre) ^((n))) to provide a modifiedtransmitted vector 406 ({tilde over (x)} _(s) ^((n))) as

{tilde over (x)} _(s) ^((n)) =S _(pre) ^((n)) ·x _(s) ^((n)).  (24)

The post-interference processing 414 removes the inter-antennainterference 404 among the receiving gateways induced as the gatewaysexperience different weather conditions 410 (w _(d) ^((n))). A linearcombination of the received gateway transmissions at the data processorthrough multiplication by G_(post) ^((n)) provides a modified receivedvector 416 ({tilde over (y)} _(g) ^((n)), as

{tilde over (y)} _(g) ^((n)) =G _(post) ^((n)) ·y _(g) ^((n)).  (25)

The downlink counterpart to the pre-interference and post-interferenceprocessing in (19) and (20) are

S _(pre) ^((n))=√{square root over (P _(d) ^((n)))}·V _(d) ^((n))Q  (26)

G _(post) ^((n))=(Λ_(d) ^((n)) {tilde over (H)} _(d) ^((n)) S _(pre)^((n)))_(left) ⁻¹  (27)

Smart Gateway Diversity Using Multiple Mimo Feeder Links

A smart gateway diversity configuration in which P diversity MIMO linksare added per N primary ones for redundancy. A beam is served by onegateway and its traffic is switched over to a diversity gateway whenexperiencing heavy rainfall. For a beam to go into outage, the beam'sgateway is placed in outage when the P diversity sites are unavailable.The following table summarizes when ground interference processing,satellite interference processing or a combination thereof may be useddepending on a link's direction (gateway to satellite (uplink) orsatellite to gateway (downlink) and rain fade conditions.

Ground Satellite Uplink - clear sky Y N Downlink - clear sky Y NUplink - SINR < acceptable SINR loss threshold Y Y Downlink - SINR <acceptable SINR loss threshold Y Y Uplink - precipitation >precipitation-induced N Y outage limit Downlink - precipitation >precipitation-induced Y N outage limit

The system may include weather-related parameters. An acceptableprecipitation-loss limit may be a threshold where precipitation and therain fade thus induced are negligible and the gateways in a clusteroperate in a default mode, for example, only post-processing mode. Theacceptable precipitation may be expressed as an acceptable SINR lossthreshold between the gateway and the satellite. For example, a loss of3 dB or less may be treated as negligible or tolerable and the systemmay continue to operate as if the LoS is a clear sky. However, lossesgreater than the threshold may be used to trigger processing by thesatellite interference processor for the affected LoS signaling. Thesatellite interference processor may generally be a pass-through toconserve satellite resources such as available power.

A precipitation-induced outage limit may be a threshold whereprecipitation and the rain fade thus induced are so excessive that, fora cluster, replacing the weather-affected gateway with an availablediversity gateway is advisable. When a gateway experiences precipitationbetween the acceptable precipitation-loss limit and theprecipitation-induced outage limit, countermeasures for the affectedgateway may include pre- and post-interference processing.

Numerical Studies

Results from extensive performance evaluations demonstrate theweather-resiliency of the various countermeasures for feeder links thatutilize LoS MIMO under linear and circular gateway formations. Theevaluation assumes a GEO satellite in an equatorial slot with longitudeθ_(s) of 97° W and orbital radius R_(s) of 42,164 km. The GEOsatellite's reflector antennas each have a diameter D of 2 meters anduniform spacing d_(s) of 6 meters. The frequency band considered is inthe V/E band. A received CNR of 24 dB is used in clear sky. Two weatherregions for the gateway clusters are evaluated with locations in Nevadaand Montana, USA.

FIG. 5A, FIG. 5B and FIG. 5C illustrate uplink SINR performance of a 3×3MIMO feeder link with a linear gateway formation when usingpre-interference processing, post-interference processing, and pre- andpost-interference processing, respectively, according to someembodiments.

FIG. 5A, FIG. 5B and FIG. 5C display performance in terms of SINR foreach of the receive antennas in a 3×3 MIMO linear configuration, locatedin Nevada and using a carrier frequency of 80 GHz, as it varies withgateway separation under clear-sky conditions. Performance is dependenton the inter-gateway separation, with a peak performance 502 achievedwith a uniform spacing between the gateways of 17 km. Similarperformances can be achieved by applying linear combination on thetransmit side (FIG. 5A) or at the receive side (FIG. 5B) or by applyinglinear combination on both the transmit and receive sides (FIG. 5C). Assuch, ground-based processing may be sufficient, relieving thecomputational burden of satellite onboard processing. Post-interferenceprocessing only solution of FIG. 5B reveals differences between theperformances as the second gateway is at the boresight whereas theothers are not depending on the separation. In comparison to SINR 504for SISO solutions, about 4.7 dB additional benefit is extracted whenusing 3×3 MIMO configuration.

FIG. 6A, FIG. 6B and FIG. 6C illustrate uplink SINR performance of a 3×3MIMO feeder link with a circular gateway formation when usingpre-interference processing, post-interference processing, and pre- andpost-interference processing, respectively, according to someembodiments.

FIG. 6A, FIG. 6B and FIG. 6C show performance in terms of SINR for eachof the receive antennas in a 3×3 MIMO circular configuration, located inNevada and using a carrier frequency of 80 GHz, as it varies withgateway separation under clear-sky conditions. Performance is dependenton the inter-gateway separation, with a peak performance 602 achievedwith a uniform spacing between the gateways of 43 km. Under a circularformation, all the gateways experience the same normalized loss due toantenna patterns. In comparison to SINR 604 for SISO solutions, about4.5 dB additional benefit is extracted when using 3×3 MIMOconfiguration.

FIG. 7A, FIG. 7B and FIG. 7C illustrate uplink SINR performance of a 3×3MIMO feeder link with a linear gateway formation when the third gatewayexperiences a 10-dB rain attenuation and using pre-interferenceprocessing, post-interference processing, and pre- and post-interferenceprocessing, respectively, according to some embodiments.

FIG. 7A, FIG. 7B and FIG. 7C illustrate the impact on SINR performancewhen a 10-dB rain attenuation affects the third gateway. At a separationof 17 km, using the post-interference processing solution in FIG. 7Boffers a degraded performance only for the attenuated gateway, sufferingfrom a 10-dB loss 706. This confirms the SINR loss anticipatedanalytically by (22). For the pre- and post-interference processingsolution in FIG. 7C, the performance is uniform across the gateways witha loss of 6 dB 708, offering an additional margin to rain of 4 dB. Thisis consistent with the SINR loss anticipated analytically by (21) whencombining pre-interference and post-interference processing.

FIG. 8A, FIG. 8B and FIG. 8C illustrate Uplink SINR performance of a 3×3MIMO feeder link with a circular gateway formation when the thirdgateway experiences a 10-dB rain attenuation and using pre-interferenceprocessing, post-interference processing, and pre- and post-interferenceprocessing, respectively, according to some embodiments.

FIG. 8A, FIG. 8B and FIG. 8C illustrate uplink SINR performance of a 3×3MIMO feeder link deploying circular formation when the third gatewayexperiences a 10-dB rain attenuation. At a spacing of 43 km, the loss inSINR 806 when adopting post-interference processing is present for theaffected gateway only, suffering from 10 dB degradation. For the pre-and post-interference processing solution in FIG. 8C, the sameperformance is achieved across the gateways, offering 4 dB additionalmargin to rain through their cooperation. The SINR loss of 10 dB for theaffected gateway when using post-interference processing and the 6-dBloss uniformly measured across gateways when combined withpre-interference processing corroborate the SINR expressions (22) and(21), respectively.

FIG. 9A and FIG. 9B illustrate uplink sum-rate performance of 3×3 MIMOfeeder link in clear sky when using a linear and circular gatewayformation, respectively, according to some embodiments.

FIG. 9A and FIG. 9B illustrate a comparison between the sum-rateachieved by the different countermeasures and the theoretical capacitybound under clear-sky conditions for a carrier frequency of 80 GHz. Ascan be seen in FIG. 9A and FIG. 9B, the capacity bound is maximized atcertain inter-gateway separations relative to inter-antenna spacingonboard the satellite. Also, the maximum capacity is approached byeither pre-interference (FIG. 9A) or post-interference (FIG. 9B)processing with separations of 17 km and 43 km for the linear andcircular formations, respectively. Also, it is shown that capacity 902of a 3×3 MIMO feeder link exceeds the sum rate capacity 904 of threeSISO feeder links by about 20%, suggesting that full degrees of freedom,in this case three, is achieved at the optimal inter-gatewayseparations.

FIG. 10A and FIG. 10B illustrate uplink sum-rate performance of 3×3 MIMOfeeder link when the third gateway experiences a 10-dB rain attenuationand using a linear and circular gateway formation, respectively,according to some embodiments.

FIG. 10 provides a comparison between the sum-rate achieved by thedifferent countermeasures and the theoretical capacity bound when thethird gateway experiences a 10-dB rain attenuation. The sum-rate is thecapacity of two uplinks using the same resources of time, carrier,orthogonality. In this case, the performance in terms of sum-rate at theoptimal separation is different when adopting different countermeasures.The theoretical capacity bound is approached by the post-interferenceprocessing as its performance degrades only for the gateway affected bythe rain attenuation. When combined with pre-interference processing,the performance is uniform across the gateways, enforcing fairness, andis better relative to that of pre-interference processing alone.

FIG. 11A and FIG. 11B illustrate capacity of 3×3 MIMO feeder link as itvaries against inter-gateway separation and orientation when using alinear and circular gateway formation, respectively, according to someembodiments.

FIG. 11A and FIG. 11B illustrate a comparison between the linear andcircular formations of a 3×3 MIMO feeder link in terms of theorientation parameter δ_(g) ^((n)) at carrier frequency of 80 GHz. Assuggested by the figure, over a wide range of orientations [−90°, 90° ],the linear formation offers only one optimal set of inter-gatewayseparation and orientation, with a minimum capacity observed whengateways are perpendicular to the line connecting the satelliteantennas. In contrast, the circular formation offers four possibleoptimal locations over the same range of orientations, providing moreflexibility in locating optimal gateway installation sites.

FIG. 12 illustrates outage probability comparison of 3×3 MIMO with SISOfeeder links, according to some embodiments.

FIG. 12 documents the outage probability computation when usingpre-interference and post-interference processing for a 3×3 MIMO feederlink with equal separation of 43 km. The long-term rain attenuationstatistics used are those of Montana. A comparison with state-of-the-artSISO is also provided. Compared with its SISO counterpart, a targetoutage probability of 0.2% can be achieved by a 3×3 MIMO feeder linkwith an additional margin of 7.2 dB when benefiting from deployingpre-interference and post-interference processing. Also shown in thefigure is the outage probability associated with the countermeasure thatuses only post-interference processing, computed based on threeindividual gateways going into outage. At a target of 0.02%, a 3×3 MIMOfeeder link provides an additional rain attenuation margin of 4.2 dBrelative to three traditional SISO feeder links.

FIG. 13 illustrates overall network outage probability comparison ofmultiple 3×3 MIMO with SISO feeder links, according to some embodiments.

FIG. 13 illustrates the overall network outage probability computationwhen deploying multiple 3×3 MIMO-enabled feeder links where 15 areprimary and one feeder link is used for diversity. This corresponds to atotal of 45 gateways deployed as primary and 3 added for diversity. Whena primary gateway experiences heavy rainfall, its traffic is re-routedto a diversity gateway. The figure indicates that for an outageprobability target of 0.01%, state-of-the-art SISO feeder links can onlytolerate a threshold SINR of 19.7 dB. In contrast, a 3×3 MIMO feederlinks can tolerate a threshold SINR of 23.8 dB, offering more than 4 dBof enhanced overall satellite network availability.

Having described preferred embodiments of a system and method (which areintended to be illustrative and not limiting), it is noted thatmodifications and variations can be made by persons skilled in the artconsidering the above teachings. It is therefore to be understood thatchanges may be made in the embodiments disclosed which are within thescope of the invention as outlined by the appended claims. Having thusdescribed aspects of the invention, with the details and particularityrequired by the patent laws, what is claimed and desired protected byLetters Patent is set forth in the appended claims.

What is claimed is:
 1. A method for providing Multi-Input Multi-Output(MIMO) feeder links for a multibeam satellite, the method comprising:receiving a Tx signal as X Tx signals on a MIMO channel with Y-antennaeas Y Rx signals, wherein each of the Y-antennae generate one of the Y Rxsignals; and ground-interference processing the X Tx signals or the Y Rxsignals to recover the Tx signal, wherein when the Y-antennae are notdisposed on a ground, pre-interference processing the X Tx signals andpost-interference processing the Y Rx signals as a pass through when arespective Signal-to-Interference-and-Noise Ratio (SINR) of each of theY Rx signals is greater than a threshold, and when the Y-antennae aredisposed on the ground, pre-interference processing the X Tx signals asa pass through and post-interference processing the Y Rx signals when arespective Signal-to-Interference-and-Noise Ratio (SINR) of each of theY Rx signals is greater than a threshold, and a channel capacity of theMIMO channel is greater than a channel capacity of a Single-InputSingle-Output (SISO) channel having resources identical to the MIMOchannel.
 2. The method of claim 1, wherein X and Y are equal.
 3. Themethod of claim 1, further comprising post-interference processing, whenthe Y-antennae are not disposed on the ground, for countermeasures whenthe respective SINR of each of the Y Rx signals is less than or equal tothe threshold.
 4. The method of claim 3, wherein the countermeasures arebased on one or more of, a weighted or non-weighted version of, aZero-Forcing (ZF) criteria, a Minimum Mean-Square Error (MMSE) criteria,or a regularized ZF (RZF) criteria.
 5. The method of claim 3, whereinthe countermeasures are based on high-quality channel state information(CSI) about signal propagation on the MIMO channel.
 6. The method ofclaim 1, wherein the Y-antennae are disposed in a Geosynchronous orbitsatellite, the respective SINR of each of the Y Rx signals less than orequal to the threshold, the post-interference processing comprisescountermeasures, the ground interference processing uses an identitymatrix, and weather between one of the multibeam satellite and theY-antennae exceeds a precipitation-induced outage limit.
 7. The methodof claim 1, wherein the Y-antennae are disposed on the ground, therespective SINR of each of the Y Rx signals less than or equal to thethreshold, the post-interference processing comprises a passthrough, thepre-interference processing uses a non-identity matrix, and weatherbetween the multibeam satellite and the Y-antennae exceeds aprecipitation-induced outage limit.
 8. The method of claim 1, whereinwhen weather, between Z of X-antennae used for transmitting and theY-antennae, exceeds a precipitation-induced outage limit, Z diversityantennae are substituted for Z of the X-antennae or the Y-antennae onthe ground, the X×Y MIMO antenna system operates as a (X−Z)×Y or X×(Y−Z)MIMO antenna system, and Z is greater than or equal to
 1. 9. The methodof claim 1, further comprising transmitting via M antennae clusters; andassociating each of the M antennae clusters with a respective Tx signal,wherein each of the M antennae clusters transmit over the MIMO channelsimultaneously, and M is greater than
 1. 10. The method of claim 9,wherein the M antennae clusters are separated from each other by adistance greater than 100 kilometers on the ground.
 11. The method ofclaim 1, wherein the Y-antennae are spaced in a substantially linearformation on the ground and spaced from one another by a distance ofless than 50 kilometers.
 12. The method of claim 1, wherein theY-antennae are spaced in a substantially circular formation on theground and spaced from one another by a distance of less than 50kilometers.
 13. The method of claim 1, wherein the Y-antennae are spacedin a substantially linear formation on a Geosynchronous orbit satellite.14. The method of claim 1, wherein the Y-antennae are spaced in asubstantially circular formation on a Geosynchronous orbit satellite.15. The method of claim 1, wherein the Y-antennae are interconnected viaa fiber or microwave link, and spaced on the ground within an acceptablerange of an optimal position.
 16. The method of claim 1, wherein the XTx signals are substantially orthogonal at the Y-antennae.